Thanks for posting this old favorite. If you google up "teddy bears picnic," up will come the link to the wiki:
http://en.wikipedia.org/wiki/Teddy_Bears'_Picnic . Very informative, with lots of follow-up potential!
I do believe that the recording you posted is the one referred to as the first (of many).
If you're as old (young?!) as I am (72), you might have listened to a radio program called "Big John and Sparky," or "No School Today." It was broadcast out of WLW-Cincinnati on Saturdays, and "The Teddy Bears Picnic" was the theme song. I can recall, imperfectly, some of the lyrics:
If you go down in the woods today
You better not go alone.
It's lovely down in the woods today,
But safer to stay at home.
Beneath the trees,
Where nobody sees,
They'll hide-and-seek as long as they please,
Today's the day the teddy bears have their picnic.
Trio:
Picnic time for teddy bears,
The little teddy bears are having a lovely time today.
Watch them catch them unawares,
And see them picnic on their holiday.
See them gaily get about,
They love to play and shout, They never have any cares.
At six o'clock their mommies and daddies will take them home to bed,
Because they're tired little teddy bears.
Musically, it's a march form, with a first and second strain followed by the trio, which in this context just means the third part of the form, not a trio in the usual sense of a piece for three performers.
Ah, the memories!